What is the Greatest Common Factor of 17208 and 17214?

Greatest common factor (GCF) of 17208 and 17214 is 6.

GCF(17208,17214) = 6

We will now calculate the prime factors of 17208 and 17214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17208 and 17214.

How to find the GCF of 17208 and 17214?

We will first find the prime factorization of 17208 and 17214. After we will calculate the factors of 17208 and 17214 and find the biggest common factor number .

Step-1: Prime Factorization of 17208

Prime factors of 17208 are 2, 3, 239. Prime factorization of 17208 in exponential form is:

17208 = 2³ × 3² × 239¹

Step-2: Prime Factorization of 17214

Prime factors of 17214 are 2, 3, 19, 151. Prime factorization of 17214 in exponential form is:

17214 = 2¹ × 3¹ × 19¹ × 151¹

Step-3: Factors of 17208

List of positive integer factors of 17208 that divides 17208 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 239, 478, 717, 956, 1434, 1912, 2151, 2868, 4302, 5736, 8604

Step-4: Factors of 17214

List of positive integer factors of 17214 that divides 17208 without a remainder.

1, 2, 3, 6, 19, 38, 57, 114, 151, 302, 453, 906, 2869, 5738, 8607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17208 and 17214. The biggest common factor number is the GCF number.
So the greatest common factor 17208 and 17214 is 6.

Also check out the Least Common Multiple of 17208 and 17214